Ge films were epitaxially grown on GaAs(100) substrates and Ga 0.88In0.12 As (100) virtual substrates using an ultrahigh vacuum/chemical vapor deposition system. The incubation time of Ge growth depends on Ga(In)As surfaces that were processed by different wet chemical solutions. Growth behaviors, such as island growth at the initial stages and selective growth into recessed regions of GaAs, were studied by transmission electron microscopy. To test the quality of Ge grown on GaAs, an n+ -Ge/p-GaAs diode was fabricated. We propose that through Ge selective epitaxial growth, Ge can be used as the source-drain of a GaAs metal-oxide-semiconductor field-effect transistor (MOSFET) to overcome some intrinsic limitations of this device.